"Every day is the best surprise party ever," says Danielle Haim, describing the past year in the life of the band that bears her surname. Indeed, when you're the buzziest group in music, the "is this really happening?" moments are going to come fast and furious. Today's surprise is the most mind-blowing yet: In the U.K., Haim's album, Days Are Gone, debuted at No. 1, ahead of Justin Timberlake. Up to this point, Danielle and her sister bandmates, Este, 27, and Alana, 21, were freaking out just mingling with pop superstars, on festival stages and in magazines. Now, they're beating those same superstars at their own game. Shit just got surreal.

"With the Justin thing, I'm his biggest fan. We were listening to a lot of FutureSex/LoveSounds while making the record, and I think he's a fucking genius," says Danielle, 24, over the phone from a sold-out tour stop in New Orleans. "It's been the most surprising, weird, crazy thing that's happened so far. It's also the best thing ever, because it's, like, our record. We worked so fucking hard on it, so it's nice to see people are listening to it and liking it."

That's an understatement: Everyone, it seems, has fallen in love with Haim—even if most still mispronounce the trio's name (it rhymes with "time"). They've been endorsed, in one form or another, by Katy Perry, A$AP Rocky, One Direction, Primal Scream and David Cameron, the friggin' British prime minister. They've gone on the road with Mumford & Sons, Vampire Weekend and Florence and the Machine. Jay Z signed them to his Roc Nation management group. And that was all back when they only had four songs out. 

The reviews for Days Are Gone, Haim's first full-length album, which dropped Sept. 30, have backed up the hype. NME called it "one of the best pop albums you'll hear all year." Pitchfork bestowed the record a coveted Best New Music tag. "If I were young and Haim had a fan club," wrote NPR critic Ken Tucker, "I'd probably join it." That's the kind of gushy admiration the band elicits, and it's no wonder: In the era of the monoculture, its music—Laurel Canyon harmonizing, rippling "Edge of Seventeen" guitars, Prince-like drums and production perched between '80s soft rock and '90s R&B—activates the closest thing to a universal pleasure center that still exists. 

On the surface, it doesn't read like a left-field success story. Three down-to-earth California girls who play their own instruments and write instantly addictive pop rock with multigenerational appeal? It sounds like an act grown in a record-company Petri dish. 

But what separates Haim from the many Internet-Age bands that end up choking on their own buzz is, the sisters really did work "so fucking hard" for this. After playing cover songs in their parents' family band and prefab pop in the Nickelodeon-approved Valli Girls, the siblings went legit in 2007, and spent the ensuing five years taking any gig they could land—including opening for a Harry Potter tribute band. ("We were the first of three at the Troubadour, and the Remus Lupins headlined," Danielle says. "Everyone was dressed up like sexy Hermione.") They recorded and scrapped 10 EPs' worth of material until hitting on the three tracks that made up 2012's Forever

From there, the tides of anticipation began to rise, but the group didn't rush to capitalize on the initial chatter. Instead, Haim sequestered itself in the studio. One year and many spins of “SexyBack” later, Days Are Gone is out, and the wait has only compounded the results.  

"There was a little pressure to release it earlier, but we knew, if it wasn't right, we weren't going to release it," Danielle says. "We knew if we took our time and experimented with sounds, people would still care. It seems like they did.” 

Album sales and the clamor for Haim's first U.S. headlining tour have certainly borne that out. (Mississippi Studios has been sold out for weeks.) But for all its confidence, the thing that'll maintain Haim long enough to make a second album is something it learned from its years of scrounging for attention: You're only as good as your last show. 

"We're still an opening band," Danielle says. "We're opening for Phoenix, so it's different types of bands—bigger bands—but we still have that same mentality, of going out and fighting for someone to listen to you.” 

SEE IT: Haim plays Mississippi Studios, 3939 N Mississippi Ave., with Io Echo, on Tuesday, Oct. 22. 9 pm. Sold out.